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A thief runs with a uniform …

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A thief runs with a uniform speed of 10metrs per second after 1 minute a police man runs after the thief to catch him he goes with a speed of 100m /minute in first minute and increases his speed by 10m /minute every succedding minute. After how many minutes the policeman will catch the thief.

Posted by Mausam Kumar 7 years, 7 months ago

CBSE > Class 10 > Mathematics

4 answers

Anurag Mishra 7 years, 7 months ago

5 minutes

Prakhar Chandra 7 years, 7 months ago

Let the police catch the thief in n min

As the thief ran 1 min before the police...time taken by the thief before being caught = (n+1) min

Distance travelled by the thief in (n+1) min = 100(n+1)m

Speed of police in 1st min=100m/min

Speed of police in 2nd min=110m/min

...3rd min = 120m/min.........so on

100,110,120,............ this forms an AP

Total distance travelled by the police in n min = n/2(2 x 100 +(n-1)10)

On catching the thief by police,distance traveled by thief= distance travelled by the police

100(n+1)= n/2(2 x 100 + (n-1)10)

100n + 100= 100n +n/2(n-1)10

100=n(n-1)5

n2 -n-20 = 0

(n-5)(n+4) = 0

n-5 = 0

n= 5 OR n= -4...(but this is not possible)

so, n= 5

Time taken by the policeman to catch the thief = 5min

Neetu Singh 7 years, 7 months ago

How ????5 min..

Aman Kumar 7 years, 7 months ago

5 min

ANSWER

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